Answer :
Final answer:
In a normal distribution, approximately 68 percent of the observations fall within one standard deviation of the mean. This is a reflection of the Empirical Rule which applies to symmetric, bell-shaped distributions. Therefore, the correct option is C.
Explanation:
For the normal distribution, the mean plus and minus one standard deviation will include about 68 percent of the observations. This is part of what is known as the Empirical Rule, which describes the percentage of observations within certain standard deviation ranges for a normally distributed set of data. The Empirical Rule states that approximately 68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and over 99% is within three standard deviations.
To provide an example, if we have a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 6, then about 68% of the observations would lie between 44 (50 - 6) and 56 (50 + 6). These thresholds of one standard deviation away from the mean encompass the majority of data points in a standard normal distribution.
The concept of the normal curve and standard deviations is crucial in statistics for understanding data dispersion and probability. It highlights how data tends to cluster around the mean, with predictable variation as you move away from the center.
